Certain plants form climbing vines. To support and control the direction in which the vines grow, plant growers build trellis systems. A conventional trellis system may include a set of strands such as wires, cables, strings, or ropes that extend across a frame made of light wooden or metal bars, bamboo poles, or plastic pipe. In the past, attempts have been made to provide trellis frames with vertically extensible elements that allow the height of the frame to be adjusted as the plants grow, as well as with horizontally extensible elements that allow the frame to be built above planting boxes or tables of different sizes. However, none of these adjustable trellis frames have been commercially successful, possibly because the adjustment mechanisms have been difficult to use. There is no currently available system that allows consumers to quickly assemble a trellis system to their own specifications, and to easily adjust, disassemble, and reconfigure the system as their needs change. The above problems are addressed by this disclosure as summarized below.